Hello.
We have a point that the line passes through and its slope.
Let's write the equation in Point-Slope Form:
y-y₁=m(x-x₁)
In this case,
y₁=2
m=[tex]\displaystyle\frac{1}{2}[/tex]
x₁=4
Plug in the values:
[tex]\mathrm{y-2=\displaystyle\frac{1}{2} (x-4)}[/tex]
This is point-slope form. Now, what about Slope-Intercept?
First, we should distribute [tex]\displaystyle\frac{1}{2}[/tex]:
[tex]\mathrm{y-2=\displaystyle\frac{1}{2} x-2}[/tex]
Add 2 to both sides:
[tex]\mathrm{y=\displaystyle\frac{1}{2} x-2+2}[/tex]
Simplify:
[tex]\mathrm{y=\displaystyle\frac{1}{2} x}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Answer:
Step-by-step explanation:
Slope intercept form: y = mx + b
here, m is the slope and b is the y-intercept.
[tex]y=\dfrac{1}{2}x+b[/tex]
The line passes through the point(4,2)
.Plugin these x ad y values in the above equation to find 'b'
[tex]2= \dfrac{1}{2}*4+b\\\\\\2=2+b\\\\b = 2 - 2[/tex]
b = 0
Equation of the line :
[tex]y =\dfrac{1}{2}x[/tex]
